Bipolar region formation in stratified two-layer turbulence

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
e-mail: warnecke@mps.mpg.de
² Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
³ Department of Astronomy, AlbaNova University Center, Stockholm University, 10691 Stockholm, Sweden
⁴ JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80303, USA
⁵ Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA
⁶ Department of Mechanical Engineering, Ben-Gurion University of the Negev, POB 653, 84105 Beer-Sheva, Israel

Received: 12 February 2015
Accepted: 14 February 2016

Abstract

Aims. This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots.

Methods. In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In most cases, it is horizontal, but a vertical and an inclined field are also considered. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process.

Results. Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around 100 across the turbulent layer. For the fluid Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. A small imposed horizontal field component is necessary to generate bipolar structures. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations.